The geometric sequence $(a_i)$ is defined by the formula: $a_i = \dfrac{1}{9} \left(-3\right)^{i - 1}$ What is $a_{5}$, the fifth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $\dfrac{1}{9}$ and the common ratio is $-3$ To find $a_{5}$ , we can simply substitute $i = 5$ into the given formula. Therefore, the fifth term is equal to $a_{5} = \dfrac{1}{9} \left(-3\right)^{5 - 1} = 9$.